Fermat

The complexity of the characterization of array probes comes from the diversity of the probe design, partly due to the piezo-composite technology which allows any shape such as Fermat surface to be achieved. We illustrate the charaeterization purpose taking three different probe examples (see figure 1) ... 

ChaC82 Chao, C-Y. Generalizations of theorems of Wilson, Fermat and Euler. J. Number Theory 15 (1982) 95-114. 

Fundamental to the understanding of optics is the Principle of Least Time, developed by Fermat ( 1650), which says that light will take the path that... 

The equivalent of the grating equation for a prism is the application of Fermat s principle to the configuration shown in Fig. 12. 

Use Lagrange s method of multipliers to derive the law of refraction of light from Fermat s principle of least time between two fixed points. 

To develop a system of mechanics from here without the introduction of any other concepts, apart from energy, some general principle that predicts the course of a mechanical change is required. This could be like the Maupertuis principle of least action or Fermat s principle of least time. It means that the actual path of the change will have an extreme value e.g. minimum) of either action or time, compared to all other possible paths. Based on considerations like these Hamilton formulated the principle that the action integral... 

He tested a number of fungicides and discovered that a solution of Fermate was the most successful of all, although solutions of Arasan and Zerlate were next in... 

Saxe Beginning Functional Analysis. Scharlau/Opolka From Fermat to... 

Following Atkins [68], the propagation of particles follows a path dictated by Newton s laws, equivalent to Hamilton s principle, that particles select paths between two points such that the action associated with the path is a minimum. Therefore, Fermat s principle for light propagation is Hamilton s principle for particles. The formal definition of action is an integral identical in structure with the phase length in physical optics. Therefore, particles are associated with wave motion, the wave-particle dualism. Hamilton s principle of least... 

Fermat s last theorem survived for 350 years as a hypothesis until English mathematician Andrew Wiles,... 

The law of geometrical optics anticipated by Hero of Alexandria was formulated by Fermat (1601-1655) as a principle of least time, consistent with Snell s law of refraction (1621). The time for phase transmission from point P to point Q along a path x(r) is given by... 

The above discussion implicitly obeys Huygens 97 principle, that each point on a spherical wavefront can be regarded as the source of a secondary wavelet (another spherical wave), as well as Fermat s98 principle of least time. 

---